I'll throw my two cents in since this is pretty much what my career looks like. I have a computer science degree, I started off in "traditional" software development roles, and I'm now a designer at GitHub.

Even during college and my first development jobs, I realized I had an unusually high interest in visual design and what would come to be known as UX. When I worked on my own projects, I naturally wanted to handle the design side and eventually I became relatively proficient at it.

I decided to go independent after a while and I freelanced for ~7 years. At first I prided myself on the fact that I could do everything. I could do all of the backend coding and I could make a nice UI. Over time, I realized that I could never be really good at everything. I decided to put more effort into improving as a designer while not completely abandoning my tech chops.

So, back to your questions. My opinion is that yes, it is possible to be equally good at everything on the spectrum as long as you're ok with the skill level across the spectrum never being super high. My colleague Kyle Kneath has a fantastic visual explanation of this idea. (Jump to slide 33 of this presentation)

As for the first question, learning how to use Sketch (probably a better use of your time than PS at this point) is certainly helpful. What I like to tell people looking to improve at design is this: start seeing the things around you. We all look at things every day, but most people don't see them. When you see something you like (whether digital, physical, etc.), ask yourself why you like it. Is it the colors? The tactile feedback? The tone of the copywriting? The subtle use of animation? Someone designed that thing. Put yourself in their shoes and ask yourself how you would have designed it. What would you have done differently and why is their version superior?

If you're interested in UX, I assume you have strong empathy skills. If you have decent developer chops + natural empathy + a desire to improve your visual design skills, you will be a very valuable member on any team. You don't need to attempt to become world class at everything, but follow what you're naturally interested in and you'll be in a great place.